Subgroups — C₂×C₄₁×#1910 #23797209

Order 10496.

1878 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#535	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#418	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#410	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1910	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
9	C₄₁×#568	—	2	2	no	—
10	C₄₁×#568	—	2	4	no	—
11	C₄₁×#568	C₂²	1	4	yes	complemented
12	C₂×#131×C₄₁	—	2	4	no	—
13	C₂²×M₁₆×C₄₁	—	2	2	no	—
14	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
15	C₄₁×#535	—	2	2	no	—
16	C₄₁×#535	—	2	2	no	—
17	C₄₁×#535	C₄	1	4	yes	complemented
18	C₄₁×#535	C₂²	1	4	yes	—
19	C₂×#127×C₄₁	C₄	1	2	yes	complemented
20	C₂×#124×C₄₁	C₄	1	2	yes	complemented
21	C₂×#121×C₄₁	—	2	2	no	—
22	C₂×#120×C₄₁	—	2	2	no	—
23	C₂×#117×C₄₁	C₂²	1	2	yes	—
24	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#418	—	2	4	no	—
26	C₄₁×#418	C₂²	1	8	yes	complemented
27	C₂×#102×C₄₁	—	2	4	no	—
28	C₄₁×#410	—	2	2	no	—
29	C₄₁×#410	C₂²	1	4	yes	complemented
30	C₂×#99×C₄₁	—	2	2	no	—
31	C₄₁×H(3,ℤ/4)	C₂²	1	8	yes	complemented
32	C₂⁵×C₄₁	—	2	1	no	—
33	C₂×#41×C₄₁	—	2	2	no	—
34	C₂×#41×C₄₁	—	2	2	no	—
35	C₂×#41×C₄₁	—	2	2	no	—
36	C₂×#41×C₄₁	—	2	2	no	—
37	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
38	C₂×#41×C₄₁	D₄	1	2	yes	—
39	C₂×#41×C₄₁	D₄	1	2	yes	—
40	C₂×#41×C₄₁	C₂³	1	2	yes	—
41	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
42	C₂²×D₄×C₄₁	—	2	4	no	—
43	C₂²×D₄×C₄₁	—	2	2	no	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	—	2	1	no	—
46	C₂²×D₄×C₄₁	—	2	1	no	—
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	—	2	2	no	—
49	C₂²×D₄×C₄₁	—	2	2	no	—
50	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
51	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
52	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
53	C₂²×D₄×C₄₁	D₄	1	2	yes	—
54	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₄₁	D₄	1	2	yes	—
56	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
57	#131×C₄₁	—	2	16	no	—
58	#131×C₄₁	—	2	16	no	—
59	C₂×M₁₆×C₄₁	—	2	4	no	—
60	C₂×M₁₆×C₄₁	—	2	8	no	—
61	C₂×M₁₆×C₄₁	—	2	2	no	—
62	C₂×M₁₆×C₄₁	—	2	8	no	—
63	C₂×M₁₆×C₄₁	—	2	2	no	—
64	C₂×M₁₆×C₄₁	—	2	2	no	—
65	C₂×M₁₆×C₄₁	—	2	2	no	—
66	C₂×M₁₆×C₄₁	D₄	1	4	yes	complemented
67	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
68	C₂²×C₈×C₄₁	—	2	4	no	—
69	C₂²×C₈×C₄₁	D₄	1	4	yes	complemented
70	#127×C₄₁	—	2	4	no	—
71	#127×C₄₁	C₂×C₄	1	8	yes	complemented
72	#124×C₄₁	—	2	4	no	—
73	#124×C₄₁	C₂×C₄	1	8	yes	complemented
74	#121×C₄₁	—	2	8	no	—
75	#121×C₄₁	—	2	8	no	—
76	#120×C₄₁	—	2	8	no	—
77	#120×C₄₁	—	2	8	no	—
78	#117×C₄₁	—	2	1	no	—
79	#117×C₄₁	—	2	1	no	—
80	#117×C₄₁	—	2	2	no	—
81	#117×C₄₁	—	2	2	no	—
82	#117×C₄₁	—	2	2	no	—
83	#117×C₄₁	C₂×C₄	1	2	yes	—
84	#117×C₄₁	C₂³	1	4	yes	—
85	#117×C₄₁	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
91	C₂×C₄²×C₄₁	—	2	2	no	—
92	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
93	#102×C₄₁	—	2	16	no	—
94	#99×C₄₁	—	2	8	no	—
95	C₂⁴×C₄₁	—	2	2	no	—
96	C₂⁴×C₄₁	—	2	2	no	—
97	C₂⁴×C₄₁	—	2	2	no	—
98	C₂⁴×C₄₁	—	4	2	no	—
99	C₂⁴×C₄₁	—	4	2	no	—
100	C₂⁴×C₄₁	—	8	4	no	—
101	C₂⁴×C₄₁	C₂²⋊C₄	1	2	yes	—
102	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
103	#41×C₄₁	—	2	4	no	—
104	#41×C₄₁	—	2	4	no	—
105	#41×C₄₁	—	2	4	no	—
106	#41×C₄₁	—	2	4	no	—
107	#41×C₄₁	—	2	4	no	—
108	#41×C₄₁	—	2	4	no	—
109	#41×C₄₁	—	2	4	no	—
110	#41×C₄₁	—	2	4	no	—
111	C₂×Q₈×C₄₁	—	2	2	no	—
112	C₂×Q₈×C₄₁	—	2	2	no	—
113	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
114	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₄₁	—	2	4	no	—
116	C₂×D₄×C₄₁	—	2	4	no	—
117	C₂×D₄×C₄₁	—	2	16	no	—
118	C₂×D₄×C₄₁	—	2	2	no	—
119	C₂×D₄×C₄₁	—	2	2	no	—
120	C₂×D₄×C₄₁	—	2	2	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂×D₄×C₄₁	—	2	4	no	—
123	C₂×D₄×C₄₁	—	2	4	no	—
124	C₂×D₄×C₄₁	—	2	4	no	—
125	C₂×D₄×C₄₁	—	2	4	no	—
126	C₂×D₄×C₄₁	—	2	4	no	—
127	C₂×D₄×C₄₁	—	2	2	no	—
128	C₂×D₄×C₄₁	—	2	4	no	—
129	C₂×D₄×C₄₁	—	4	2	no	—
130	C₂×D₄×C₄₁	—	4	1	no	—
131	C₂×D₄×C₄₁	—	4	1	no	—
132	C₂×D₄×C₄₁	—	4	2	no	—
133	C₂×D₄×C₄₁	—	4	2	no	—
134	C₂×D₄×C₄₁	—	4	1	no	—
135	C₂×D₄×C₄₁	—	4	2	no	—
136	C₂×D₄×C₄₁	—	4	1	no	—
137	C₂×D₄×C₄₁	—	8	8	no	—
138	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
139	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
140	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
141	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
142	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₄₁	—	2	2	no	—
144	C₂²×C₄×C₄₁	—	2	2	no	—
145	C₂²×C₄×C₄₁	—	2	2	no	—
146	C₂²×C₄×C₄₁	—	2	2	no	—
147	C₂²×C₄×C₄₁	—	2	2	no	—
148	C₂²×C₄×C₄₁	—	4	2	no	—
149	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
150	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
151	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₄₁	#41	1	2	yes	—
160	C₂²×C₄×C₄₁	#41	1	2	yes	—
161	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
162	M₁₆×C₄₁	—	2	16	no	—
163	M₁₆×C₄₁	—	2	4	no	—
164	M₁₆×C₄₁	—	2	4	no	—
165	M₁₆×C₄₁	—	2	4	no	—
166	M₁₆×C₄₁	—	2	4	no	—
167	C₂×C₈×C₄₁	—	2	16	no	—
168	C₂×C₈×C₄₁	—	2	4	no	—
169	C₂×C₈×C₄₁	—	2	4	no	—
170	C₂×C₈×C₄₁	C₂×D₄	1	8	yes	complemented
171	C₄⋊C₄×C₄₁	—	2	2	no	—
172	C₄⋊C₄×C₄₁	—	2	2	no	—
173	C₄⋊C₄×C₄₁	—	2	4	no	—
174	C₄⋊C₄×C₄₁	—	4	2	no	—
175	C₂²⋊C₄×C₄₁	—	2	2	no	—
176	C₂²⋊C₄×C₄₁	—	2	2	no	—
177	C₂²⋊C₄×C₄₁	—	2	16	no	—
178	C₂²⋊C₄×C₄₁	—	2	4	no	—
179	C₂²⋊C₄×C₄₁	—	4	2	no	—
180	C₄²×C₄₁	—	2	2	no	—
181	C₄²×C₄₁	—	2	4	no	—
182	C₄²×C₄₁	—	4	2	no	—
183	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
184	C₂³×C₄₁	—	2	2	no	—
185	C₂³×C₄₁	—	2	2	no	—
186	C₂³×C₄₁	—	2	4	no	—
187	C₂³×C₄₁	—	4	2	no	—
188	C₂³×C₄₁	—	4	4	no	—
189	C₂³×C₄₁	—	4	8	no	—
190	C₂³×C₄₁	—	4	4	no	—
191	C₂³×C₄₁	—	4	2	no	—
192	C₂³×C₄₁	—	4	4	no	—
193	C₂³×C₄₁	—	4	2	no	—
194	C₂³×C₄₁	—	8	8	no	—
195	C₂³×C₄₁	—	8	4	no	—
196	C₂³×C₄₁	—	8	4	no	—
197	C₂³×C₄₁	—	8	8	no	—
198	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
200	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×C₄₁	#121	1	2	yes	—
202	C₂³×C₄₁	#121	1	2	yes	—
203	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₄₁	—	2	4	no	—
205	Q₈×C₄₁	—	2	4	no	—
206	D₄×C₄₁	—	2	8	no	—
207	D₄×C₄₁	—	2	8	no	—
208	D₄×C₄₁	—	2	4	no	—
209	D₄×C₄₁	—	2	8	no	—
210	D₄×C₄₁	—	2	4	no	—
211	D₄×C₄₁	—	4	2	no	—
212	D₄×C₄₁	—	4	2	no	—
213	D₄×C₄₁	—	4	2	no	—
214	D₄×C₄₁	—	4	2	no	—
215	D₄×C₄₁	—	4	4	no	—
216	D₄×C₄₁	—	8	16	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	2	4	no	—
220	C₂×C₄×C₄₁	—	2	4	no	—
221	C₂×C₄×C₄₁	—	2	4	no	—
222	C₂×C₄×C₄₁	—	2	4	no	—
223	C₂×C₄×C₄₁	—	2	4	no	—
224	C₂×C₄×C₄₁	—	4	4	no	—
225	C₂×C₄×C₄₁	—	4	4	no	—
226	C₂×C₄×C₄₁	—	8	4	no	—
227	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
228	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
231	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
232	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
233	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₄₁	#120	1	2	yes	—
235	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
236	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
237	C₂×C₄×C₄₁	#121	1	2	yes	—
238	C₂×C₄×C₄₁	#121	1	2	yes	—
239	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
240	C₂×C₄×C₄₁	#123	1	2	yes	—
241	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
242	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
246	C₈×C₄₁	—	2	8	no	—
247	C₂×#1910	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂²×C₄₁	—	2	2	no	—
249	C₂²×C₄₁	—	2	4	no	—
250	C₂²×C₄₁	—	2	4	no	—
251	C₂²×C₄₁	—	4	1	no	—
252	C₂²×C₄₁	—	4	2	no	—
253	C₂²×C₄₁	—	4	1	no	—
254	C₂²×C₄₁	—	4	4	no	—
255	C₂²×C₄₁	—	4	8	no	—
256	C₂²×C₄₁	—	4	4	no	—
257	C₂²×C₄₁	—	4	4	no	—
258	C₂²×C₄₁	—	8	2	no	—
259	C₂²×C₄₁	—	8	4	no	—
260	C₂²×C₄₁	—	8	8	no	—
261	C₂²×C₄₁	—	8	8	no	—
262	C₂²×C₄₁	—	8	4	no	—
263	C₂²×C₄₁	#386	1	1	yes	characteristic
264	C₂²×C₄₁	#386	1	2	yes	—
265	C₂²×C₄₁	#386	1	1	yes	characteristic
266	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×C₄₁	C₂×#121	1	2	yes	—
268	C₄×C₄₁	—	2	4	no	—
269	C₄×C₄₁	—	4	4	no	—
270	C₄×C₄₁	—	8	4	no	—
271	C₄×C₄₁	#386	1	1	yes	characteristic
272	C₄×C₄₁	#386	1	1	yes	characteristic
273	C₄×C₄₁	#386	1	2	yes	—
274	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
275	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
276	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
277	C₂×#568	C₂×C₄₁	1	1	yes	characteristic, complemented
278	C₂×#535	C₂×C₄₁	1	1	yes	characteristic
279	C₂×#418	C₂×C₄₁	1	2	yes	complemented
280	C₂×#410	C₂×C₄₁	1	1	yes	characteristic, complemented
281	#1910	C₂×C₄₁	1	8	yes	direct product factor
282	C₂×H(3,ℤ/4)	C₂×C₄₁	1	2	yes	complemented
283	C₂×C₄₁	—	2	1	no	—
284	C₂×C₄₁	—	2	2	no	—
285	C₂×C₄₁	—	2	1	no	—
286	C₂×C₄₁	—	2	2	no	—
287	C₂×C₄₁	—	4	4	no	—
288	C₂×C₄₁	—	8	4	no	—
289	C₂×C₄₁	#1910	1	2	yes	direct product factor
290	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
291	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
292	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
293	#568	—	2	2	no	—
294	#568	—	2	4	no	—
295	#568	C₂²×C₄₁	1	4	yes	complemented
296	C₂×#131	—	2	4	no	—
297	C₂²×M₁₆	—	2	2	no	—
298	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
299	#535	—	2	2	no	—
300	#535	—	2	2	no	—
301	#535	C₄×C₄₁	1	4	yes	complemented
302	#535	C₂²×C₄₁	1	4	yes	—
303	C₂×#127	C₄×C₄₁	1	2	yes	complemented
304	C₂×#124	C₄×C₄₁	1	2	yes	complemented
305	C₂×#121	—	2	2	no	—
306	C₂×#120	—	2	2	no	—
307	C₂×#117	C₂²×C₄₁	1	2	yes	—
308	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
309	#418	—	2	4	no	—
310	#418	C₂²×C₄₁	1	8	yes	complemented
311	C₂×#102	—	2	4	no	—
312	#410	—	2	2	no	—
313	#410	C₂²×C₄₁	1	4	yes	complemented
314	C₂×#99	—	2	2	no	—
315	H(3,ℤ/4)	C₂²×C₄₁	1	8	yes	complemented
316	C₄₁	C₂×#1910	1	1	yes	characteristic, direct product factor, Sylow
317	C₂⁵	—	2	1	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
323	C₂×#41	D₄×C₄₁	1	2	yes	—
324	C₂×#41	D₄×C₄₁	1	2	yes	—
325	C₂×#41	C₂³×C₄₁	1	2	yes	—
326	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
336	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
337	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
338	C₂²×D₄	D₄×C₄₁	1	2	yes	—
339	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
340	C₂³×C₄	D₄×C₄₁	1	2	yes	—
341	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
342	#131	—	2	16	no	—
343	#131	—	2	16	no	—
344	C₂×M₁₆	—	2	4	no	—
345	C₂×M₁₆	—	2	8	no	—
346	C₂×M₁₆	—	2	2	no	—
347	C₂×M₁₆	—	2	8	no	—
348	C₂×M₁₆	—	2	2	no	—
349	C₂×M₁₆	—	2	2	no	—
350	C₂×M₁₆	—	2	2	no	—
351	C₂×M₁₆	D₄×C₄₁	1	4	yes	complemented
352	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
353	C₂²×C₈	—	2	4	no	—
354	C₂²×C₈	D₄×C₄₁	1	4	yes	complemented
355	#127	—	2	4	no	—
356	#127	C₂×C₄×C₄₁	1	8	yes	complemented
357	#124	—	2	4	no	—
358	#124	C₂×C₄×C₄₁	1	8	yes	complemented
359	#121	—	2	8	no	—
360	#121	—	2	8	no	—
361	#120	—	2	8	no	—
362	#120	—	2	8	no	—
363	#117	—	2	1	no	—
364	#117	—	2	1	no	—
365	#117	—	2	2	no	—
366	#117	—	2	2	no	—
367	#117	—	2	2	no	—
368	#117	C₂×C₄×C₄₁	1	2	yes	—
369	#117	C₂³×C₄₁	1	4	yes	—
370	#117	C₂³×C₄₁	1	2	yes	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	4	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₄²	—	2	2	no	—
377	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
378	#102	—	2	16	no	—
379	#99	—	2	8	no	—
380	C₂⁴	—	2	2	no	—
381	C₂⁴	—	2	2	no	—
382	C₂⁴	—	2	2	no	—
383	C₂⁴	—	4	2	no	—
384	C₂⁴	—	4	2	no	—
385	C₂⁴	—	8	4	no	—
386	C₂⁴	C₂²⋊C₄×C₄₁	1	2	yes	—
387	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
388	#41	—	2	4	no	—
389	#41	—	2	4	no	—
390	#41	—	2	4	no	—
391	#41	—	2	4	no	—
392	#41	—	2	4	no	—
393	#41	—	2	4	no	—
394	#41	—	2	4	no	—
395	#41	—	2	4	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
399	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	16	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	—	8	8	no	—
423	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
424	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
425	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
426	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
427	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
435	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
436	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
439	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
444	C₂²×C₄	#41×C₄₁	1	2	yes	—
445	C₂²×C₄	#41×C₄₁	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
447	M₁₆	—	2	16	no	—
448	M₁₆	—	2	4	no	—
449	M₁₆	—	2	4	no	—
450	M₁₆	—	2	4	no	—
451	M₁₆	—	2	4	no	—
452	C₂×C₈	—	2	16	no	—
453	C₂×C₈	—	2	4	no	—
454	C₂×C₈	—	2	4	no	—
455	C₂×C₈	C₂×D₄×C₄₁	1	8	yes	complemented
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	16	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	4	2	no	—
468	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	4	no	—
474	C₂³	—	4	8	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	4	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	8	8	no	—
480	C₂³	—	8	4	no	—
481	C₂³	—	8	4	no	—
482	C₂³	—	8	8	no	—
483	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
484	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
485	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
486	C₂³	#121×C₄₁	1	2	yes	—
487	C₂³	#121×C₄₁	1	2	yes	—
488	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	2	4	no	—
491	D₄	—	2	8	no	—
492	D₄	—	2	8	no	—
493	D₄	—	2	4	no	—
494	D₄	—	2	8	no	—
495	D₄	—	2	4	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	4	no	—
501	D₄	—	8	16	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	8	4	no	—
512	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
513	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
514	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
515	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
516	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
517	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
518	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
519	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
520	C₂×C₄	#120×C₄₁	1	2	yes	—
521	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
522	C₂×C₄	#121×C₄₁	1	2	yes	—
523	C₂×C₄	#121×C₄₁	1	2	yes	—
524	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
525	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
526	C₂×C₄	#123×C₄₁	1	2	yes	—
527	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
530	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
531	C₈	—	2	8	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	8	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	8	2	no	—
543	C₂²	—	8	4	no	—
544	C₂²	—	8	8	no	—
545	C₂²	—	8	8	no	—
546	C₂²	—	8	4	no	—
547	C₂²	C₄₁×#386	1	1	yes	characteristic
548	C₂²	C₄₁×#386	1	2	yes	—
549	C₂²	C₄₁×#386	1	1	yes	characteristic
550	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
551	C₂²	C₂×#121×C₄₁	1	2	yes	—
552	C₄	—	2	4	no	—
553	C₄	—	4	4	no	—
554	C₄	—	8	4	no	—
555	C₄	C₄₁×#386	1	1	yes	characteristic
556	C₄	C₄₁×#386	1	1	yes	characteristic
557	C₄	C₄₁×#386	1	2	yes	—
558	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
559	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
560	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
561	C₂	—	2	1	no	—
562	C₂	—	2	2	no	—
563	C₂	—	2	1	no	—
564	C₂	—	2	2	no	—
565	C₂	—	4	4	no	—
566	C₂	—	8	4	no	—
567	C₂	C₄₁×#1910	1	2	yes	direct product factor
568	C₂	C₂×C₄₁×#386	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	#386
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₄₁×#568	C₂	semidirect
3. C₂×C₄₁×#418	C₂	semidirect
4. C₂×C₄₁×#410	C₂	semidirect
5. C₄₁×#1910	C₂	direct (N × H)
6. C₂×C₄₁×H(3,ℤ/4)	C₂	semidirect
11. C₄₁×#568	C₂²	semidirect
17. C₄₁×#535	C₄	semidirect
19. C₂×#127×C₄₁	C₄	semidirect
20. C₂×#124×C₄₁	C₄	semidirect
26. C₄₁×#418	C₂²	semidirect
29. C₄₁×#410	C₂²	semidirect
31. C₄₁×H(3,ℤ/4)	C₂²	semidirect
66. C₂×M₁₆×C₄₁	D₄	semidirect
69. C₂²×C₈×C₄₁	D₄	semidirect
71. #127×C₄₁	C₂×C₄	semidirect
73. #124×C₄₁	C₂×C₄	semidirect
170. C₂×C₈×C₄₁	C₂×D₄	semidirect
247. C₂×#1910	C₄₁	direct (N × H)
277. C₂×#568	C₂×C₄₁	semidirect
279. C₂×#418	C₂×C₄₁	semidirect
280. C₂×#410	C₂×C₄₁	semidirect
281. #1910	C₂×C₄₁	direct (N × H)
282. C₂×H(3,ℤ/4)	C₂×C₄₁	semidirect
289. C₂×C₄₁	#1910	direct (N × H)
295. #568	C₂²×C₄₁	semidirect
301. #535	C₄×C₄₁	semidirect
303. C₂×#127	C₄×C₄₁	semidirect
304. C₂×#124	C₄×C₄₁	semidirect
310. #418	C₂²×C₄₁	semidirect
313. #410	C₂²×C₄₁	semidirect
315. H(3,ℤ/4)	C₂²×C₄₁	semidirect
316. C₄₁	C₂×#1910	direct (N × H)
351. C₂×M₁₆	D₄×C₄₁	semidirect
354. C₂²×C₈	D₄×C₄₁	semidirect
356. #127	C₂×C₄×C₄₁	semidirect
358. #124	C₂×C₄×C₄₁	semidirect
455. C₂×C₈	C₂×D₄×C₄₁	semidirect
567. C₂	C₄₁×#1910	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄₁×#568	2
C₂×C₄₁×#535	2
C₂×C₄₁×#418	2
C₂×C₄₁×#410	2
C₄₁×#1910	2
C₂×C₄₁×H(3,ℤ/4)	2
C₂×#1910	41

Subgroups — C2×C41×#1910 #23797209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1910 #23797209